No system-size anomalies in entropy of bcc iron at Earth\u2019s inner-core conditions

Andrew J Schultz,Sabry G Moustafa,David A Kofke

doi:10.1038/s41598-018-25419-3

Andrew J Schultz, Sabry G Moustafa + Show 1 more

Open Access

https://doi.org/10.1038/s41598-018-25419-3

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Abstract

New molecular modeling data show that the entropy of bcc iron exhibits no system-size anomalies, implying that it should be feasible to compute accurate free energies of this system using first-principles methods without requiring a prohibitively large number of atoms. Conclusions are based on rigorous calculations of size-dependent free energies for a Sutton-Chen model of iron previously fit to ab initio calculations, and refute statements recently appearing in the literature indicating that the size of the simulation cell is critical for stabilization of the bcc phase.

Highlights

Data from molecular simulations of iron at Earth’s inner-core conditions have been reported in ref.[1] (hereafter referred to as (I))
Our primary interest is to test whether the free energy is extensive for small-to-moderate values of N, so instead we perform this calculation for successively larger systems, repeatedly doubling the system size, and we examine whether the successive differences are consistent with an extensive free energy
We find that the free energy is extensive, and there is no anomalous behavior of Sbcc with system size

Summary

Introduction

Data from molecular simulations of iron at Earth’s inner-core conditions have been reported in ref.[1] (hereafter referred to as (I)). For force-field models (such as SC) it is possible to evaluate the free energy very accurately (within any approximation inherent in the molecular model), enabling the observations made in (I) to be rigorously tested It is still a challenging calculation because at the pressures of interest bcc is mechanically (and thermodynamically) unstable at T = 0 K, so we cannot apply a conventional approach based on integration from low temperature[2]; further, results from methods using integration from a noninteracting cell model or Einstein lattice[3] should work but might be viewed with some doubt because they completely suppress diffusion along part of the integration path, and the switch from non-diffusive to diffusive behavior could be problematic

Methods

Results

Conclusion